A321492 Numbers that can be written as (x + y)(x^2 + y^2), x > y > 0, in at least two ways.

12325, 98600, 117720, 146705, 206312, 263840, 332775, 378505, 400945, 500200, 651456, 687245, 734400, 741845, 773800, 788800, 799240, 941760, 1173640, 1327360, 1533195, 1540625, 1650496, 1735105, 1836680, 1943240, 2048320, 2050880, 2110720, 2217280, 2662200, 2704360, 2965685

Offset

1,1

Comments

See A321491 for numbers of the form (x+y)(x^2+y^2) = A321490(x,y) with x > y > 0.

Links

Table of n, a(n) for n=1..33.

Geoffrey B. Campbell, (m+n)(m²+n²) in two different ways, LinkedIn Number Theory Group, Aug. 2018

Example

12325 = (13+16)(13^2+16^2) = (3+22)(3^2+22^2).
98600 = (26+32)(26^2+32^2) = (6+44)(6^2+44^2).
117720 = (21+39)(21^2+39^2) = (8+46)(8^2+46^2).
146705 = (24+41)(24^2+41^2) = (14+47)(14^2+47^2).
206312 = (15+53)(15^2+53^2) = (32+42)(32^2+42^2).
263840 = (6+62)(6^2+62^2) = (33+47)(33^2+47^2).

Prog

(PARI) A321492_list(L=1e6)={my(S=[], T=List(), t); for(m=2, sqrtn(L, 3), while(#S&&S[1]<=m^3, S=S[^1]); for(n=1, m-1, if(L<t=(m+n)*(m^2+n^2), next(2), setsearch(S, t), listput(T, t); S=setminus(S, [t]), S=setunion(S, [t])))); Set(T)}

Crossrefs

Cf. A321490, A321491.

Sequence in context: A077186 A077189 A277947 * A237782 A248717 A184472

Adjacent sequences: A321489 A321490 A321491 * A321493 A321494 A321495

Keyword

nonn

Author

Geoffrey B. Campbell and M. F. Hasler, Nov 22 2018

Status

approved